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Riemann made some famous contributions to modern analytic number theory. In a single short paper, the only one he published on the subject of number theory, he investigated the zeta function that now bears his name, establishing its importance for understanding the distribution of prime numbers.
Riemann hypothesis, in number theory, hypothesis by German mathematician Bernhard Riemann concerning the location of solutions to the Riemann zeta function, which is connected to the prime number theorem and has important implications for the distribution of prime numbers.
Riemann's thesis studied the theory of complex variables and, in particular, what we now call Riemann surfaces. It therefore introduced topological methods into complex function theory.
Bernhard Riemann (1826 - 1866) - Biography - MacTutor History of ...
Bernhard Riemann made profound, far-sighted discoveries with lasting consequences for mathematics and our understanding of space, gravity, and time. Riemannian geometry completely reformed the field of geometry and became the mathematical foundation of Einstein's general theory of relativity.
One mathematician who found the presence of Dirichlet a stimulus to research was Bernhard Riemann, and his few short contributions to mathematics were among the most influential of the century.
The subject founded by this work is Riemannian geometry. Riemann found the correct way to extend into n dimensions the differential geometry of surfaces, which Gauss himself proved in his theorema egregium. The fundamental objects are called the Riemannian metric and the Riemann curvature tensor.
